bag-of-tokens.html

<p>You have an initial <strong>power</strong> of <code>power</code>, an initial <strong>score</strong> of <code>0</code>, and a bag of <code>tokens</code> where <code>tokens[i]</code> is the value of the <code>i<sup>th</sup></code> token (0-indexed).</p>

<p>Your goal is to maximize your total <strong>score</strong> by potentially playing each token in one of two ways:</p>

<ul>
	<li>If your current <strong>power</strong> is at least <code>tokens[i]</code>, you may play the <code>i<sup>th</sup></code> token face up, losing <code>tokens[i]</code> <strong>power</strong> and gaining <code>1</code> <strong>score</strong>.</li>
	<li>If your current <strong>score</strong> is at least <code>1</code>, you may play the <code>i<sup>th</sup></code> token face down, gaining <code>tokens[i]</code> <strong>power</strong> and losing <code>1</code> <strong>score</strong>.</li>
</ul>

<p>Each token may be played <strong>at most</strong> once and <strong>in any order</strong>. You do <strong>not</strong> have to play all the tokens.</p>

<p>Return <em>the largest possible <strong>score</strong> you can achieve after playing any number of tokens</em>.</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input:</strong> tokens = [100], power = 50
<strong>Output:</strong> 0
<strong>Explanation</strong><strong>:</strong> Playing the only token in the bag is impossible because you either have too little power or too little score.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input:</strong> tokens = [100,200], power = 150
<strong>Output:</strong> 1
<strong>Explanation:</strong> Play the 0<sup>th</sup> token (100) face up, your power becomes 50 and score becomes 1.
There is no need to play the 1<sup>st</sup> token since you cannot play it face up to add to your score.
</pre>

<p><strong>Example 3:</strong></p>

<pre>
<strong>Input:</strong> tokens = [100,200,300,400], power = 200
<strong>Output:</strong> 2
<strong>Explanation:</strong> Play the tokens in this order to get a score of 2:
1. Play the 0<sup>th</sup> token (100) face up, your power becomes 100 and score becomes 1.
2. Play the 3<sup>rd</sup> token (400) face down, your power becomes 500 and score becomes 0.
3. Play the 1<sup>st</sup> token (200) face up, your power becomes 300 and score becomes 1.
4. Play the 2<sup>nd </sup>token (300) face up, your power becomes 0 and score becomes 2.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= tokens.length &lt;= 1000</code></li>
	<li><code>0 &lt;= tokens[i],&nbsp;power &lt; 10<sup>4</sup></code></li>
</ul>